We use the well-established oscillating mirror model (OMM) [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]} to analyze the plasma dynamics around the surface, and we neglect other mechanisms [8]} for the particle acceleration. Because the pair plasma yield in experiments is so far small (\(\alpha \ll 1\) ) [9]}, [10]}, [11]}, the electron population governs the mirror oscillation, and the positrons can be treated as test particles. For convenience, the theoretical analysis and the simulations are presented in the moving frame. In the following equations, the time, space and electric field are normalized by \(\omega _{0}^{-1}\) , \(c/\omega _{0}\)  and \(m_e\omega _{0}c/e\) , respectively. Here, \(c\)  is the speed of light in vacuum; \(e\)  and \(m_e\)  are the charge and mass of an electron; \(\omega _{0}\)  is the laser frequency. The governing equation for electron motion is given by [1]}:
\(\frac{d^2X_e}{dt^2}=-\frac{\Gamma _d^3\omega _{pe}^2}{\gamma _{e}}X_e+\frac{a^2-a\tan \theta }{\gamma _{e}^2d_s}\) 
